JP0155283
Recent Reflectometry Results from the UCLA Plasma Diagnostics Group
M. Gilmore, E.J. Doyle, S. Kubota, X.V. Nguyen, W.A. Peebles, T.L. Rhodes, and L. Zeng Electrical Engineering Department, University of California, Los Angeles, CA, USA
Presented at the Fifth Reflectometry Workshop, Toki, Gifu, Japan, 5-7 March 2001.
Abstract
The UCLA Plasma Diagnostics Group has an active ongoing reflectometry program. The program is threefold, including 1) profile and 2) fluctuation measurements on fusion devices (DEH-D, NSTX, and others), and 3) basic reflectometry studies in linear and laboratory plasmas that seek to develop new measurement capabilities and increase the physics understanding of reflectometry. Recent results on the DIH-D tokamak include progress toward the implementation of FM reflectometry as a standard density profile diagnostic, and correlation length measurements in QDB discharges that indicate a very different scaling than normally observed in L-mode plasmas. The first reflectometry measurements in a spherical torus (ST) have also been obtained on NSTX. Profiles in NSTX show good agreement with those of Thomson scattering. Finally, in a linear device, a local magnetic field strength measurement based on O- X correlation reflectometry has been demonstrated to proof of principle level, and correlation lengths measured by reflectometry are in good agreement with probes.
- 7 - I. INTRODUCTION
Reflectometry can provide both electron density profiles with high spatial and temporal resolution, and density fluctuation measurements from the plasma edge to the core. One proven method for density profile measurement is the FM radar technique.1'2 The UCLA group currently operates FM radar systems on both the DIII-D tokamak and NSTX spherical torus. In Section II, recent profile measurements from DIII-D and NSTX are shown, and progress in implementing FM relfectometry as a standard diagnostic is briefly discussed. Section III presents correlation reflectometry measurements from DIII-D. Radial correlation lengths, Ar, are compared in DIH-D L-mode and Quiescent Double Barrier (QDB) discharges,3'4 and are found to exhibit different scalings. Two aspects of basic reflectometry studies are discussed in Section IV. First, the development of a magnetic field strength, | B ], diagnostic based on dual mode (O-X) correlation reflectometry is presented. It is shown that, in these experiments, | B | could be determined simultaneously with the radial correlation length, Ar. Second, comparisons between radial correlation lengths measured by homodyne reflectometry and a Langmuir probe array are presented. Good agreement is found between the reflectometer and probe.
II. FM PROFILE MEASUREMENTS
Significant progress has been made toward implementing profile reflectometry as a standard diagnostic on the DIII-D tokamak. Automatic profile analysis has been demonstrated, system spatial coverage has been optimized via polarization flexibility, and upgraded data acquisition has significantly extended the time coverage. The profile reflectometers on DIII-D are Q- (33-50 GHz) and V-band (50-75 GHz) FM radars,5'6 that operate in either 0- or X-mode.7 The data acquisition system and analysis software have been upgraded to allow profiles to be measured every 10 ms for an entire 5 s discharge, and analyzed between shots. O- mode measurements are able to access the plasma core, while X-mode scans the edge. The 0-mode system has been particularly important in measuring the steep profiles found to occur in operating modes with internal transport barriers (ITB) with good time resolution. Fig. 1 shows an example of the time evolution of the electron density at an ITB. In order to construct X-mode profiles, the start of reflection from the right-hand cut-off must be identified. For O-mode in the core, a reliable fit to Thomson Scattering (TS) profiles at the edge must be available. Furthermore, in cases where the O-mode begins to transmit above cut-off, this point in the time record must be identified. Software is now in place and operating to automatically determine this information, and to reconstruct the profiles between shots.7 Note that the large volume of profiles, up to 10,000 per discharge, requires an automated analysis system. Currently, however, operator intervention is still required to obtain profiles showing detailed agreement with those of the TS system. Development of a fully automatic system is ongoing. An FM profile reflectometer, consisting of three O-mode systems in the bands 12-18 GHz, 20-32 GHz and 33-50 GHz, has also been installed on the National Spherical Torus Experiment (NSTX),8 and initial results have been obtained. All three NSTX systems utilize circular horn antennas, and rotating waveguide joints so that the polarization angle can be adjusted manually. During operation, the polarization is typically aligned with the expected edge magnetic field pitch angle. Figure 2 shows a recent reflectometer profile from NSTX together with Thomson scattering measurements. As can be seen, there is good agreement between the two measurements over most of the outer half of the plasma. Note that this is the first reflectometry measurement in an ST device. These initial results are encouraging since there were concerns about problems with reflectometry in the ST's resulting from O-X mode conversion due to the large magnetic field shear.9
III. CORRELATION MEASUREMENTS IN DIII-D
Although some questions regarding the interpretation of fluctuation and correlation data remain,1 correlation reflectometry is now a mature enough diagnostic to be used reliably for physics studies in magnetically confined plasmas. Figures 3 and 4 show two recent and interesting correlation results from DIII-D.3'11 These measurements were made with a heterodyne frequency tunable V-band (50-75 GHz) system located on the outboard midplane.12 First, Fig. 3 plots radial correlation length, Ar, measurements in DIII-D in typical L-mode and QDB discharges. The QDB discharge is a high performance mode that exhibits both edge and core transport barriers. The core barrier, as well as sheared flow due to radial electric field, exists over a large region of the core plasma.3'4 In the L-mode case, Ar exhibits a scaling with either the poloidal ion sound gyroradius, pes (i.e. the gyroradius using Te instead of Tj), or approximately 5-8 times the total sound gyroradius, ps. In contrast, the QDB case Ar's are significantly smaller than the L-mode scaling, which is consistent with reduced turbulent transport step size and improved confinement.
- 9 - Second, a comparison between reflectometer measurements and a 3D toroidal electrostatic gyrokinetic simulation13 is shown in Fig. 4. This comparison is an early result from a program to make experiment-model comparisons in detail. The initial simulated plasmas have been circular (DIII-D plasmas are shaped), however comparisons with shaped plasmas are now under way. Measured ne, T,, and q profiles were used in the simulation. Two simulation results are shown, both with and without self- generated, or zonal, flows included. Without zonal flows, correlation lengths are seen to be very long - in a fact a large fraction of the total 65 cm minor radius. When zonal flows are included, Ar can be seen to reduce to values near the experimental measurements. Although the agreement is intriguing, this is a very early stage of the comparison and more work remains. Nevertheless, this seems a clear indication of the importance of zonal flow effects in gyrokinetic modeling.
IV. BASIC REFLECTOMETRY STUDIES
A. Dual mode (O-X) correlation reflectometry
Basic studies of dual mode correlation reflectometry have been conducted in the LArge Plasma Device (LAPD) at UCLA.14'15 In addition to fluctuation/correlation length measurements, O-X reflectometry can provide a local, nonperturbing measurement of | B I. If O- and X-modes are launched and received through the same pair of antennas, one might expect the cross correlation of both fluctuating signals to maximize when the two reflecting layers overlap spatially. If each signal comes from its respective cut-off layer, then the X-mode frequency corresponding to cut-off at the same spatial location as the O-mode can be written in terms of fo and fx,
(1) where f0 and fx are the O- and X-mode frequencies respectively, fc is the electron cyclotron frequency, fp is the electron plasma frequency, and the right-hand cutoff, fR, has been taken for X-mode. Since fx and fo are known from the cross-correlation, IB | can be determined from Eq. (1). In practice, it was found that O-X cross-correlation peaked at an X-mode frequency (for fixed O-mode) less than fR. Fig. 5 shows the results of a typical cross-correlation of homodyne signals, (Iolx), where I =
Acos
GHz. Amplitude,
-10- GHz respectively. In all cases fx,pk; determined from amplitude, phase, and homodyne signals were equal to within the error bars.
Figure 6 shows the X-mode frequency of peak cross-correlation vs. magnetic field for fixed f0 = 11.0
GHz. As can be seen, fx>Pk lies below the right-hand cutoff in every case. Therefore, | B | cannot be determined from the simple formula, (1). However, it has been found that fx,pk can be accurately reproduced by a one-dimensional full wave model (code),14 as shown in Fig. 6. In order to accurately
determine fx,pk , the code requires inputs of Ln, the density gradient scale length (= ((l/n)dn/dx)''), and
Akr, the radial k-spectral width of the plasma fluctuations, S(kr) « exp{ kf /&k?}. Note that Akr is
measured directly in an O-X correlation experiment, since for a Guassian k-spectrum, Akr =2^2Ibr, where Ar is the 1/e radial correlation length. Experiment and model show good agreement with variation 14 15 of these parameters, though the range of Akr studied was limited. ' A practical |B | diagnostic would use the ID model, run iteratively, to determine B at cut-off from
measured fx,Pk and Akr, together with Ln from another diagnostic (e.g. a profile reflectometer). In the LAPD experiments, the accuracy of B was 5%, which was dominated by statistical error. It is likely that statistical error will dominate any measurement, and must be carefully assessed in any experiment. In a
hot plasma, a knowledge of Te might also be required for a relativistic correction to fR. An effect found in the O-X experiment, which is not predicted by the code, is that the maximum 14 15 cross-correlation value decreases with magnetic field strength. ' In the LAPD experiments, pox = 0.65 maximum at 0.05 T, decreasing to pox =* 0.4 at 0.2 T. The reasons for this are not yet understood and may be due to 2D effects, but, practically, this may limit the diagnostic to low B-field cases (B ~ 0.1 T).
B. Reflectometer-Probe Comparisons
Detailed comparisons of turbulent radial correlation lengths measured by reflectometry and probes in the LAPD have also been made.10 A plot comparing Ar from homodyne reflectometry to that of a probe array is shown in Fig. 7. Here Ar is taken as the 1/e length. As can be seen, there is good agreement, to within 10-15%, between reflectometer and probe in O-O, X-X, as well as O-X modes. The measured correlation lengths fell in the range 0.6 < ArA^< 1.2, or 0.7 < Ar/W^iry^ 1.3, where XQ is the reflectometer vacuum wavelength and WA^ is the Airy width.15 Note that correlation lengths less than the vacuum wavelength were accurately measured. Homodyne reflectometer and probe measurements also showed good agreement in power spectra and coherency in overall character, while phase signals showed agreement only in cases of low fluctuation
11- levels. In cases of high fluctuation levels, the phase was found to undergo a series of multi-radian phase discontinuities, or "jumps" (see ref. [16] for definitions of "low" and "high"). In these cases, the power spectra were found to approach an f2 dependence, and Ar was much shorter than the corresponding probe measurements. These observations are consistent with the Random Phase Screen Model of reflectometry.16 Finally, when a limited number of such phase jumps existed, they could be filtered out to recover power spectra and correlation lengths consistent with probe measurements.15
V. SUMMARY
Recent reflectometry results from the UCLA Plasma Diagnostics Group have been presented. FM density profile measurements have been presented from DIII-D and NSTX. Radial correlation measurements from DIII-D, now being used for physics studies, were also shown. Finally, basic reflectometry work on the linear LAPD on the development of a |B| measurement based on O-X correlation reflectometry, and comparisons with probes have been discussed.
ACKNOWLEDGEMENTS
The authors would like to thank the DIII-D, LAPD, and NSTX teams, particularly R.E. Bell, D. Johnson and B. LeBlanc for supplying the NSTX Thomson scattering data. Thanks also to J.-N. Leboeuf for his contributions of gyrokinetic modeling. This work was supported by the U.S. Department of Energy under grants No. DE-FG03-86ER-532225 and DE-FG03-99ER54527.
REFERENCES
1 E.J. Doyle et al., in Diagnostics for Thermonuclear Fusion Reactors, ed. P.E. Stott, G. Gorini and E. Sindoni, Plenum Press, New York, 117-132 (1996). 2 C. Laviron, et al Plasma Phys Cont Fusion 38, 905 (1996). 3 E.J. Doyle, et al paper IAEA-CN-77/EX6/2, 18th IAEA Fusion Energy Conf, Sorrento Italy. Also accepted for publication in Nucl Fusion; 4 C M Greenfield et al submitted to Phys Rev Lett 5 K.W. Kim et al Rev Sci Instrum 66, 1229 (1995); 6 K.W. Kim et al Rev Sci Instrum 68, 466 (1997). 7 L. Zeng et al Rev Sci Instrum 72, 320 (2001).
-12- 8 S. Kubota et al Rev Sci Instrum 72, 348 (2001). 9 M. Nagatsu, T. Hayashi and T Tokishima, Jpn J Appl Phys 1 34, 3708 (1995). 10 M. Gilmore, W.A. Peebles and X.V. Nguyen, Plasma Phys Cont Fusion 42, LI (2000). "TL Rhodes et al 27th EPS Conf on Cont Fusion and Plasma Phys, Budapest, 12-16 June 2000, ECA Vol 24B (2000), 564. 12 T.L. Rhodes et al Rev Sci Instrum 63, 4661 (1992). 13 J.-N. Leboeuf et al Phys Plasmas 7, 1795 (2000). 14 M. Gilmore, W.A. Peebles and X.V. Nguyen, Plasma Phys Cont Fusion 42, 655 (2000). 15 M. Gilmore, W.A. Peebles and X.V. Nguyen, Rev Sci Instrum 72, 293 (2001). 16 R. Nazikian and E. Mazzucato, Rev Sci Instrum 66, 392 (1995).
Figure Captions
FIG. 1. Example of the time development of a steep, localized internal transport barrier (ITB) in electron density, in a DIII-D negative central shear (NCS) discharge. The portion of the profile determined by the reflectometer system is shown by open circles.
FIG. 2. Electron density profiles in NSTX vs. major radius measured by O-mode FM reflectometry (line) and Thomson scattering (triangles). Shot 104503, 97-100 ms.
FIG. 3. Radial correlation lengths in the DHI-D core as a function of plasma radius (flux coordinates) in 3 4 cases of L-mode and QDB ' plasmas. Lines indicate the poloidal sound gyroradius, pe)S, in each case.
FIG. 4. Comparison of radial correlation lengths from measurements in DIII-D and Gyrokinetic simulations, with and without zonal (self-generated) flows included.
FIG. 5. Homodyne O-X cross-correlation coefficient, pox, vs. X-mode frequency, fx. Error bars denote
95% confidence intervals. f0 = 11.0 GHz, B = 0.10 T. Right-hand cut-off fR = 12.47±0.03 GHz.
FIG. 6. X-mode frequency of peak cross-correlation fx,pk vs. magnetic field: experiment (phase) and simulation. f0 = 11.0 GHz in each. Dashed line indicates the right-hand cut-off frequency fR corresponding to fp = 11.0 GHz.
FIG. 7. Homodyne reflectometer 1/e radial correlation length vs. those measured by a Langmuir probe array in the LAPD.
-13- 7 1 ' ' | * ' ' | ' ' ' 1 ' ' ' . e ?~*' 1.0 s : "E 6 0) 1.0 s ; ^0 1.0 s 5 : o Reflectometer Data : 4
3 Dens i 2 ro n o 1 LJJ 0.2 0.4 0.6 0.8 1 1.2 p (flux surface co-ord)
Figure 1
„ 2.0 m E o 2 1.5 i—x * 1.0 ^ c CD Q \ I c 0.5 E- ~—^~ Reflectometry o • Thomson Scattering CD 0.0 20 40 60 80 100 120 140 160 Radius [cm]
Figure 2
— 14 — 12.0 1 . • • 1 1 • • • 1 • • • • 1 • 1 1 ' a Ar, L-mode •
10.0 1 • • 1 Ar, QDB ' L-mode - 8 pe a -° s pe, QDB ! s -I—> ;V S 4.0 Is ™ m m 1 [ 2.0 - T mMI'S
%m •. • i • • • • 0.0 ,. i. 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 p (flux surface co-ord)
Figure 3
6 20
15 CD r—ic o • 1—I •4—> 10 3 • Experiment fa A Simulation, no self-generated flow o • Simulation, with self-generated flow ^ 5
0 0.4 0.5 0.6 0.7 0.8 0.9 p (flux surface co-ordinate)
Figure 4
-15- o
11 11.5 12 12.5 13 13.5 X-mode Frequency (GHz)
Figure 5
fR o Experiment ,set 1 14 i- • . . i • > i i . > . o Experiment, set 2 co --. o Experiment, set 3 - ® N 13.5 - —*—-code Q. X O -— >> c 13 - o o c T: CD CO 12.5 -- y / Fit to code J cu co "O co points ' O O f O 11-5 X : 9
11 iii i i i i . i , i 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 Magnetic Field (Tesla)
Figure 6
-16- E 0 O-mode o • X-mode jjj 2-5
1.5 2 2.5 Probe Array (cm)
Figure 7
-17-